The graph of $x^{2} + y = 10$ and the graph of $x + y = 10$ intersect in two points, then the distance between the points is .....

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\sqrt{2}

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Solution

The correct option is C $\sqrt{2}$
$G i v e n e q u a t i o n s a r e x^{2} + y = 10......... (i) a n d x + y = 10.......... (i i) S u b t r a c t i n g e q u a t i o n (i i) f r o m e q u a t i o n (i) w e g e t x^{2} - x = 0 ⟹ x (x - 1) = 0 ⟹ x = (0, 1) S u b s t i t u t i n g x = 0 i n e q u a t i o n (i i) w e g e t y = 10 a n d s u b s t i t u t i n g x = 1 i n e q u a t i o n (i i) w e g e t y = 9 ∴ p o i n t s o f i n t e r s e c t i o n a r e (x_{1}, y_{1}) = (0, 10) a n d (x_{2}, y_{2}) = (1, 9) ∴ D i s t a n c e b e t e e n t h e m d = \sqrt{{(x_{1} - x_{2})}^{2} + {(y_{1} - y_{2})}^{2}} = \sqrt{{(0 - 1)}^{2} + {(10 - 9)}^{2}} = \sqrt{2} u n i t s A n s - O p t i o n C$

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Similar questions

x^{2} + y = 10

x + y = 10

| y | = x + 1

(x - 1)^{2} + y^{2} = 4

x^{2} + y^{2} = 7

x^{2} - y^{2} = 1

y = x^{2}

y = 3 x^{2}

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